Information on Result #844074
Linear OOA(8107, 1048580, F8, 2, 18) (dual of [(1048580, 2), 2097053, 19]-NRT-code), using OOA 2-folding based on linear OA(8107, 2097160, F8, 18) (dual of [2097160, 2097053, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8106, 2097159, F8, 18) (dual of [2097159, 2097053, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8107, 1048580, F8, 3, 18) (dual of [(1048580, 3), 3145633, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (89, 107, 1048580)-net over F8 | [i] | ||